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If you have been following me around, you know that my main interests are general topology, set theory, and destroying users who post nothing but inane gibberish. The last is certainly not the least!

Projects I'd like to spend some time on:

  1. replace all occurrences of "Erdös" and "Erdos" by "Erdős"
  2. completely separate the and tags (i.e., empty this list).

comment Proving a injectivity in a separable Hausdorff space.
One fact that would help shorten this exposition (and is perhaps implicit in what you have written above) is the following: if $D \subseteq X$ is dense and $U \subseteq X$ is open, then $\overline{ U \cap D } = \overline{U}$. (And this does not rely on any separation axiom holding in $X$.)
answered Existence of Nested Countable Neighborhood Basis
awarded  general-topology
answered A topological space which is Frechet but not Strictly-Frechet.
answered Cardinality of $\lim_{k\to\infty}\mathbb N^k$ vs. $\mathbb N^\infty$
revised Prove that there exists a constant C such that $[z^n]\exp(z/(1-z)) = O(\exp(C\sqrt{n}))$
rolled back to a previous revision
answered Give an example of non-normal subspace of a normal space.
revised Is this an example of a sequential non-Fréchet–Urysohn space?
some corrections
answered Is this an example of a sequential non-Fréchet–Urysohn space?
comment Is this an example of a sequential non-Fréchet–Urysohn space?
Also, would the basic open neighbourhoods of $( \frac{1}{n} , 0 )$ be of the form $\{ ( \frac{1}{n} , 0 ) \} \cup \{ (\frac{1}{n} , \frac{1}{k} ) : k \geq j \}$ for some $j > 0$? (I.e., open neighbourhoods of these points don't necessarily include points from any other vertical section.)
comment Is this an example of a sequential non-Fréchet–Urysohn space?
Are the singletons $\{ ( \frac{1}{i} , \frac{1}{k} ) \}$ open? (If so, it's easier to just say that these points are isolated.)
revised Complex numbers confused!!
deleted 51 characters in body
comment left Haar measure and right Haar measure on ax+b group
Posting the same question multiple times is highly against the site rules.
comment One question about open sets in topology
What is the exact definition of an open set (in a metric space) given by your topology instructor? (The point here, I believe, is that this topology question gives you another equivalent way to define open in a metric space. That this matches up with another definition you have already seen is a bonus: the two were actually talking about the same thing, even if defined differently.)
answered Is every Extremally Disconnected Hausdorff Space Regular?
comment Finite Set of Models
@Nagase: No, it doesn't require infinitely long formulas. I just pick some finite number of sentences from $\mathscr{S}$, and then form a sentence (of finite length) from these finitely many sentences determined by the true-false patterns in the given models. But I do this for all choices of finitely many sentences from $\mathscr{S}$, so I will end up with an infinite collection $\Gamma$ of sentences. (Also, the models themselves could be infinite, I just have finitely many of them.)
revised Question concerning a statement about separability
added 757 characters in body
answered Question concerning a statement about separability
answered Stone-Čech compactification using ultrafilters
comment Construction of the field of real numbers within $ZF$
The usual construction of the real line (from the rationals, and of the rationals from the integers and of ...) involves absolutely no Choice. See this previous question.